A short survey on preconditioning techniques in spectral calculations

Two decades ago collocation methods for high accuracy solutions of partial differential equations seemed applicable only to special classes of problems with simple geometries, regular solutions, absence of numerical round-off errors, etc. The usefulness of these methods in engineering problems was very much in question. The situation has changed with many obstacles having been removed which prevented spectral methods to be used with maximum performance. We briefly review a key element in this change: the use of preconditioning techniques. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved